Theoria combinationis observationum erroribus minimis obnoxiae
By Carl Friedrich Gauss
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Citations in the corpus
- signSGD: compressed optimisation for non-convex problems (2018, methodology): “Recall Gauss’ inequality for unimodal random variable X with mode ν and expected squared deviation from the mode τ2 (Gauss, 1823; Pukelsheim, 1994): P[”
- Data Assimilation for Numerical Weather Prediction: A Review (2009, background): “The concept of background field goes back to Gauss[125,126].”
- Predictive Resource Management for Wearable Computing (2003, methodology): “We use recursive least-squares regression with exponential decay [36], a modification of the well-known linear regression method [15].”
- Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting (2002, methodology): “The assumption of Gaussian error for the inliers is equivalent to the commonly used least squares principal of Gauss (1821), in which the estimate is chosen that minimizes the sum of the squared errors (cid:9) e 2 i : In Bayesian terms this is equivalent to assuming a zero mean Normal distribution…”
- In Defense of One-Vs-All Classification (2004, unknown): “The mathematics of finding a linear function that minimizes the square loss over a set of data was first derived by Gauss (1823).”
- An Update on the Hirsch Conjecture (2009, background): “Last but not least, counting integer points in polytopes with integer vertex coordinates has applications ranging from number theory and representation theory to cryptography, integer programming, and statistics [5, 16].”
- On the Variance of the Adaptive Learning Rate and Beyond (2019, background): “Adam-2k Adam-vanilla RAdam Adam-warmup Fast and stable optimization algorithms are what generations of researchers have been pursuing (Gauss, 1823; Cauchy, 1847).”